# Research Seminar Algebraic Geometry

**New instances of Vojta’s Main Conjecture via Newton-Okounkov bodies and K-(in)stability**

### Organizer: D. Greb

The goal of the seminar is to understand the relation between Nevanlinna theory and Vojta’s conjecture in Diophantine Geometry on the one side and notions of birational geometry related to linear series and K-stability of Fano varieties on the other side, based on the recent paper arXiv:1901.07942 of Grieve.

**Program:**has been distributed via eMail; write to daniel.greb@uni-due.de to get a copy

**Recommendation:** For an in-depth introduction to Vojta’s conjecture, the contribution of Vojta to the following volume of lecture notes (which you can download freely if you access it via a UDE-IP-address) is highly recommended: Vojta-survey

No. | Date | Speaker | Title |
---|---|---|---|

01 | 11.04. | Daniel Greb | Overview and distribution of talks |

02 | 18.04. | Anna Piwatz | Basics of Nevanlinna Theory |

03 | 25.04. | Nils Plewe | Cartan’s Theorem |

04 | 02.05. | Vytas Paskunas | Absolute values and heights on projective spaces |

05 | 09.05. | Heer Zhao | (Local) Weil functions and height functions with respect to ample divisors |

06 | 16.05. | Lukas Pottmeyer | Height functions with respect to big divisors, proximity functions, Vojta’s conjecture and the Arithmetic General Theorem |

07 | 23.05. | Tim Kirschner | Basics on Okounkov bodies |

08 | 06.06 | Daniel Greb / Martin Schwald | Concave transforms of Okounkov bodies |

09 | 27.06. | Michael Wong | K-stability, Kähler-Einstein metrics, and the work of Fujita |

10 | 04.07. | Georg Hein | Vojta’s conjecture for K-unstable Fanos (following Grieve) |

11 | 11.07. | Program discussion for next term |